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If it thumps each time you accelerate and again when you decelerate or when it shifts, it could be broken motor mount(s). I agree with the motor mounts OR do you mean the thumping you hear/feel when you have a tire that is out of round, broken tire belting or the wheel weight has fallen off? If this is the case take your Jeep to a tire center and have them drive the jeep to check out what they say.

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Q: Why would a 96 Grand jeep Cherokee start thumping when accelerating and decelerating what could this be from?
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